CONDUCTORS AND INSULATORS
Definitions
Conductors
An electrical conductor is any material through which electrical current flows easily.
Most metals are good electrical conductors, with silver the best and copper second.
Their atomic structure allows free movement of the outer most orbital electrons.
Copper wire is generally used for practical conductors because it costs much less than
the silver. The purpose of using a conductor is to carry electric current with minimal
opposition.
Semiconductors
Carbon is considered a semiconductor, conducting less than metal conductors but
more than insulators. In the same group are germanium and silicon, which are
commonly used for transistors and other semiconductor components. The degree of
doping in semiconductors makes a large difference in conductivity. To a point, more
doping leads to higher conductivity. Practically all transistors are made of silicon.
Superconductors
Superconductivity is a property of certain materials for which the electrical resistance
of becomes exactly zero below a characteristic temperature. The electrical resistivity
of a metallic conductor decreases gradually as the temperature is lowered. However,
in ordinary conductors such as copper and silver, this decrease is limited by impurities
and other defects. Even near absolute zero (0 K = -273 °C), a real sample of copper
shows some resistance. Despite these imperfections, in a superconductor the
resistance drops abruptly to zero when the material is cooled below its critical
temperature. An electric current flowing in a loop of superconducting wire can persist
indefinitely with no power source.
In 1986, it was discovered that some ceramic materials have critical temperatures
above 90 K (−183 °C). These high-temperature superconductors renewed interest in
the topic because of the prospects for improvement and potential room-temperature
superconductivity. From a practical perspective, even 90 kelvins is relatively easy to
reach with readily available liquid nitrogen (which has a boiling point of 77 kelvins),
resulting in more experiments and applications.
Insulators
An insulator is any material that resists or prevents the flow of electric charge, such as
electrons. The resistance of an insulator is very high, typically hundreds of mega
ohms or more. An insulator provides the equivalent of an open circuit with practically
infinite resistance and almost zero current. It is from a material with atoms in which
the electrons tend to stay in their own orbits and hence cannot conduct electricity
easily. Insulators can be useful when it is necessary to prevent the current flow. In
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addition, for applications requiring the storage of electric charge, as in capacitors, a
dielectric material must be used because a good conductor cannot store any charge.
An insulating material, such as glass, plastic, rubber, paper, air, or mica, is also called
dielectric, meaning it can store electric charge.
Atomic structures that effect the properties of conductors and insulators are
illustrated in Figure 1.
Figure 1 Atomic structure of conducting and insulating materials
Wire Conductors
Types of Wire Conductors
Most wire conductors are copper due to its low cost, although aluminum and silver
are also used sometimes. The copper may be tinned with a thin coating of solder,
which gives a silvery appearance. Tinned wire is easier to solder for connections. The
wire can be solid or stranded. Solid wire is made up of only one conductor. If it bent
or flexed repeatedly, solid wire may break. Therefore solid wire is used in places
where bending and flexing is not encountered. House wiring is a good example of the
use of solid wire. Stranded wire is made up of several individual strands put together
in a braid. Some uses for stranded wire include telephone cords, extension cords and
speaker wire, to name a few. Figure 2 shows wire conductors for variety of
applications.
Stranded wire is flexible, easier to handle, and less likely to develop an open
break. Sizes for stranded wire are equivalent to sum of areas for the individual
strands. For instance, two strands of No. 30 wire corresponds to solid No. 27 wire.
Very thin wire, such as No. 30, often has an insulating coating of enamel or
shellac. It may look like copper, but the coating must be scrapped off the ends to
make a good connection. This type of wire is used for small coils.
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Figure 2 Wires and cables used for various applications
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Heavier wires generally are in an insulating sleeve, which may be rubber or one
of many plastic materials. General purpose wire for connecting electronic components
is generally plastic coated hookup wire of No. 20 gage. Hookup wire that is bare
should be enclosed in an insulating sleeve called spaghetti.
Figure 3 Types of wires and cables
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Twisted pairs are used for small signal applications in electronics. They may or
may not be shielded as illustrated in Figure 4. They are good in preventing magnetic
field pickups. The shielded ones are used especially in low noise applications.
Figure 4 Shielded and unshielded twisted pairs
The braided conductor
shown in Figure 5 is used
for very low resistance. It is
wide for low R and thin for
flexibility, and braiding
provides many strands. A
common application is a
grounding connection,
which must have very low R.
Figure 4 Braided conductors
Wire Cable
Two or more conductors in a common covering form a cable. Each wire is insulated
from the others. Cables often consist of two, three, ten, or many more pairs of
conductors, usually color coded to help to identify the conductor at both ends of a
cable.
Transmission Lines
A transmission line is a cable setup used to carry electrical signals in various
applications. Constant spacing between two conductors through the entire length
provides a transmission line. Common examples are the coaxial cable, the twin lead
and ribbon cable. The coaxial cable with outside diameter of 1/4 inch is generally
used for the signals in cable television. In construction, there is an inner solid wire,
insulated from metallic braid that serves as the other conductor. The entire assembly
is covered by an outside plastic jacket. In operation, the inner conductor has the
desired signal voltage with respect to ground, and metallic braid is connected to
ground to shield the inner conductor against interference. Coaxial cable, therefore, is a
shielded type of transmission line. Single core and dual core coaxial cables are shown
in Figure 6.
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Figure 6 Single and dual core caoxial cables
With
twin-lead
wire,
two
conductors are embedded in plastic to
provide constant spacing (Figure 7).
This type of line is commonly used in
television for connecting the antenna to
the receiver. In this application, the
spacing is 5/8 inch between wires of
No. 20 gage size, approximately. This
line is not shielded.
Figure 7 Twin-lead TV antenna wire
The ribbon cable in Figure 8, has multiple conductors but not in pairs. This cable
is used for multiple connections to a computer and associated equipment.
Figure 8 The ribbon cable for connecting computer peripherals
Standard Wire Gage Sizes
Table 1 lists the standard wire sizes in the system knows as the American Wire Gage
(AWG) expressed in metric system. The gage numbers specify the size of a round
wire in terms of its diameter and cross-sectional area. Note the following three points:
1. As the gage number increase from 1 to 40, the diameter and the circular area
decrease. Higher gage numbers indicate thinner wire sizes.
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Table 1 American Wire Gage (AWG) table in metric
2. The circular area doubles for every three gage sizes. For example, No. 10 wire
has approximately twice the area of No. 13 wire.
3. The higher the gage number and thinner the wire, the greater the resistance of
the wire for any given length.
In typical applications, hookup wire for electronic circuits with current of the
order of milliamperes in generally about No. 22 gage. For this size, 0.5 to 1 A is the
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maximum current the wire can carry without excessive heat. House wiring for circuits
where the current is 5 to 15 A is usually No. 14 gage. Minimum sizes for house
wiring are set by local electricity codes which are usually guided by the National
Electrical Code published by the National Fire Protection Association.
Properties of Wire Conductors
Conductor Ampacity
The ampacity of a conductor, that is, the amount of current it can carry, is related to
its electrical resistance: a lower-resistance conductor can carry more current. The
resistance, in turn, is determined by the material the conductor is made from (as
described above) and the conductor's size. For a given material, conductors with a
larger cross-sectional area have less resistance than conductors with a smaller crosssectional area. The economical factor plays an important role in selecting conductors
in industrial (large) scale applications. Aluminum is lighter and cheaper that copper
and it carries almost the same current as of copper for a given weight of the material.
Hence, aluminum is mostly preferred in high voltage transmission lines as the
electrical conductor.
For bare conductors, the ultimate limit is the point at which power lost to
resistance causes the conductor to melt. Aside from fuses, most conductors in the real
world are operated far below this limit, however. For example, household wiring is
usually insulated with PVC insulation that is only rated to operate to about 60 °C,
therefore, the current flowing in such wires must be limited so that it never heats the
copper conductor above 60 °C, causing a risk of fire. Other, more expensive
insulations such as Teflon or fiberglass may allow operation at much higher
temperatures.
Wire Resistance
Electrical resistivity (also known as resistivity, specific electrical resistance, or
volume resistivity) is a measure of how strongly a material opposes the flow of
electric current. A low resistivity indicates a material that readily allows the
movement of electric charge. The SI unit of electrical resistivity is the ohm meter
[Ωm]. It is commonly represented by the Greek letter ρ (rho).
Electrical conductivity or specific conductance is the reciprocal quantity, and
measures a material's ability to conduct an electric current. It is commonly
represented by the Greek letter σ (sigma). Its SI unit is Siemens per meter (S·m−1).
Many resistors and conductors have a uniform cross section with a uniform flow of
electric current and are made of one material.
In a hydraulic analogy, increasing the diameter of a pipe reduces its resistance to
flow, and increasing the length increases resistance to flow (and pressure drop for a
given flow).
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•
•
•
A conductor such as a metal has high conductivity and a low resistivity.
An insulator like glass has low conductivity and a high resistivity.
The conductivity of a semiconductor is generally intermediate, but varies
widely under different conditions, such as exposure of the material to electric
fields or specific frequencies of light, and, most important, with temperature
and composition of the semiconductor material.
The resistance of a wire conductor is directly proportional to its length and
inversely proportional to its cross sectional area. Hence, the longer a wire, the higher
its resistance. More work must be done to make electron drift from one end to the
other. However, the greater the diameter of the wire, the less the resistance, since
there are more free electrons in the cross sectional area. As a formula,
𝑅𝑅 = 𝜌𝜌
𝑙𝑙
𝐴𝐴
Where R (Ω) is the total resistance, l (m) the length, A (m2) the cross-sectional
area, and ρ (Ω.m) the specific resistance or resistivity of the conductor. The factor ρ
then enables the resistance of different materials to be compared according to their
nature without regard to different lengths or areas. Higher values of ρ means more
resistance. Resistivity of metals that are most commonly used in electrical engineering
applications is given in Table 2 for two temperatures.
Table 2 Resistivity and temperature coefficient of metals of general interest in electrical engineering
Element
Graphite (carbon)
Aluminum
Vanadium
Chromium
Iron
Nickel
Copper
Zinc
Silver
Tungsten
Platinum
Gold
Symbol
ρ at 293 K
ρ at 500 K
(227° C)
C
Al
V
Cr
Fe
Ni
Cu
Zn
Ag
W
Pt
Au
(20° C)
1375x10-8 Ωm
26.5 nΩm
197 nΩm
125 nΩm
96.1 nΩm
69.3 nΩm
16.78 nΩm
59 nΩm
15.87 nΩm
52.8 nΩm
105 nΩm
22.14 nΩm
49.9 nΩm
348 nΩm
201 nΩm
237 nΩm
177 nΩm
30.9 nΩm
108.2 nΩm
28.7 nΩm
103 nΩm
183 nΩm
39.7 nΩm
Temperature
coefficient α (/°C)
-0.0003
0.0043
0.0060
0.0059
0.0040
0.0038
0.0038
0.0044
0.0038
0.0037
Source:
http://en.wikipedia.org/wiki/Electrical_resistivities_of_the_elements_(data_page)
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Resistance Changes with Temperature
Resistance changes with temperature and how it does is indicated by a temperature
coefficient with symbol alpha (α). Although α is not exactly constant, the resistance
Rm at a temperature Tm is indicated by
𝑅𝑅𝑚𝑚 = 𝑅𝑅0 (1 + 𝛼𝛼(𝑇𝑇𝑚𝑚 − 𝑇𝑇0 ))
Where R0 is the resistance at T0.
All metals in their pure form, such as copper and tungsten, have positive
temperature coefficients. In practical terms, a positive α indicates that heat increases
R in a wire thereby the current I through the wire is reduced for a specified applied
voltage. Carbon and all semiconductors, including germanium and silicon, have
negative temperature coefficients. Some metal alloys, such as constantan and
manganin have a value zero for α. The temperature coefficient for metals of general
interest is given in the last column of Table 2.
Example: Let's take a look at an example circuit to see how temperature can affect
wire resistance, and consequently circuit performance:
This circuit has a total wire resistance (wire 1 + wire 2) of 30 Ω at standard
temperature. Setting up a table of voltage, current, and resistance values we get:
At 20o Celsius, we get 12.5 volts across the load and a total of 1.5 volts (0.75 + 0.75)
dropped across the wire resistance. If the temperature were to rise to 35o Celsius, we
could easily determine the change of resistance for each piece of wire. Assuming the
use of copper wire (α = 0.004041) we get:
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Recalculating our circuit values, we see what changes this increase in temperature
will bring:
As you can see, voltage across the load went down (from 12.5 volts to 12.42 volts)
and voltage drop across the wires went up (from 0.75 volts to 0.79 volts) as a result of
the temperature increasing. Though the changes may seem small, they can be
significant for power lines stretching miles between power plants and substations,
substations and loads. In fact, power utility companies often have to take line
resistance changes resulting from seasonal temperature variations into account when
calculating allowable system loading.
Skin Effect
Skin effect is the tendency of an alternating
electric current (AC) to distribute itself within a
conductor with the current density being largest
near the surface of the conductor, decreasing at
greater depths. In other words, the electric
current flows mainly at the "skin" of the
conductor, at an average depth called the skin
depth. The skin effect causes the effective
resistance of the conductor to increase at higher
frequencies where the skin depth is smaller, thus Figure 9 An illustartion of the skin effect
reducing the effective cross-section of the
conductor. Figure 9 illustrates the distribution of electrical current through the crosssection of a current carrying conductor in DC, AC and high frequency applications.
The skin effect is due to opposing eddy currents induced by the changing
magnetic field resulting from the alternating current. At 60 Hz in copper, the skin
depth is about 8.5 mm. At high frequencies the skin depth may be much smaller.
Increased AC resistance due to the skin effect can be mitigated by using specially
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woven Litz wire (Figure 10). Because the interior of a large conductor carries so little
of the current, tubular conductors such as pipe can be used to save weight and cost. In
copper, the skin depth can be seen to fall according to the square root of frequency as
given in Table 3.
Table 3 Skin depth versus frequency
Frequency Skin depth (μm)
60 Hz
8470
10 kHz
660
100 kHz
210
1 MHz
66
10 MHz
21
100 MHz
6.6
Figure 10 The Litz wire
Review Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Why the elements named as "conductors" conduct electricity easily?
What are the three best conductors?
Why copper is the mostly used conductor?
Why the bare copper wire is not used (why it is used with some sort of
covering/coating)?
What is a superconductor?
Why a stranded wire is preferred to solid core wire?
Why we use twisted pairs of wires?
Why we use shielded wires?
Why we use constant spacing between pairs of signal wires?
Why we don't use thick solid conductors at high frequency AC applications?
Questions
1. No. 14 gage copper wire is used for house wiring. It's weight is 18.5 gram/meter. It's
resistance is 0.00827 Ω/m at 20 °C. The temperature coefficient of copper is 0.004
/°C. What will be the resistance of 10 m wire at
a. 20 °C
b. 60 °C
2. How much is the voltage drop across the wire in the above question is the current is
4 A at
a. 20 °C
b. 60 °C
c. Assume that the wire was warming up by 2 °C as the current through it was
1 A. How much is the maximum current allowed if the plastic covering melts
at 60 °C?
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